We consider social choice problems where a society must choose a subset from a set of objects. Specifically, we characterize the families of strategy-proof voting procedures when not all possible subsets of objects are feasible, and voters' preferences are separable or additively representable.

We study the problem of a society choosing a subset of new members from a finite set of candidates (as in Barber?Sonnenschein, and Zhou, 1991). However, we explicitly consider the possibility that initial members of the society (founders) may want to leave it if they do not like the resulting...